In closing arguments on Tuesday at the manslaughter trial of a New York City police officer charged in the shooting of an unarmed man, the prosecution presented a new argument to jurors: The officer did not mistakenly fire a bullet that ricocheted off a wall and killed Akai Gurley, who was walking down the stairs of a Brooklyn housing project, as the defense has argued.

Instead, the officer, Peter Liang, had seen Mr. Gurley, 28, while on a routine patrol and aimed, a prosecutor argued in State Supreme Court in Brooklyn. “He pointed his gun,” Joe Alexis, an assistant district attorney said, “and shot Akai Gurley.”

The argument was a departure from the prosecution’s theme during the previous days of the trial, in which Officer Liang, 28, was painted as reckless, inept and craven, appearing to care only about his job in the minutes after firing, not whether anyone had been hurt.

The bullet from Officer Liang’s gun hit a wall, Mr. Alexis suggested during closing arguments, because the officer missed. “The bullet shot very close to where Akai Gurley stood,” he said, “and ripped through his heart.”

The shooting took place on Nov. 20, 2014, at the Louis H. Pink houses in the East New York neighborhood of Brooklyn, where Officer Liang, a rookie police officer, was assigned to patrol. In testimony on Monday, Officer Liang said he had been startled by a noise and flinched, inadvertently causing the gun to go off.

In his closing argument, Robert E. Brown, a lawyer for Officer Liang, portrayed him as a novice who brandished his gun inside the stairwell, where the lights were not working, because the police are trained that such areas are perilous. The prosecution has argued that patrolling with an unholstered gun was reckless in an area used by building residents.

To convict Officer Liang of manslaughter, the jurors would have to find that he had recklessly caused the death, Justice Danny K. Chun told them before they began deliberations late Tuesday afternoon. They would have to conclude that Officer Liang’s conduct created a substantial or unjustifiable risk that Mr. Gurley would be killed, and that in a “gross deviation” from a reasonable person’s conduct, he was aware of that risk and consciously disregarded it, the judge said.

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Officer Peter Liang, left, after testifying during his trial on Monday.CreditBryan R. Smith for The New York Times

Officer Liang has testified that he did not realize anyone had been shot until minutes after he fired, when he inspected the staircase in search of his bullet and found Mr. Gurley, on a landing several floors down, his girlfriend frantically trying to revive him. He has also been charged with official misconduct for failing to provide CPR to Mr. Gurley.

The government contended that the officer had violated rules that police officers must obey in two ways: by failing to adhere to police duties and by violating Mr. Gurley’s lawful right to such aid. On Tuesday, after closing arguments, Justice Chun said the prosecution had not shown that Officer Liang was bound by law to render aid and threw out that portion of the charge.

His lawyer, Mr. Brown, said in his closing arguments that Officer Liang had in fact radioed for help the night of the shooting. A recording of a police radio call introduced into evidence by the prosecution shows that while Officer Liang did transmit a radio report of the shooting, he did not ask for an ambulance.

Mr. Brown said that to find Officer Liang guilty of official misconduct, the jury would have to determine that he knowingly did not perform his duties, to obtain a benefit or deprive another of a benefit. He asked the jury, “What possible benefit could he have for not rendering aid to Mr. Gurley?”

Mr. Brown characterized Officer Liang as brave, even heroic, for entering the dark staircase. “When he got to that stairwell,” Mr. Brown said to the jury, “he didn’t say, ‘They don’t pay me enough to go in there.’ But he opened the door. And unfortunately he got startled, and we ended up here.”

“What happened here is a terrible tragedy,” he added. “But it’s not a crime.”

In contrast, Mr. Alexis, who brandished Officer Liang’s gun during closing arguments, spoke in a booming voice at times as he dismissed any notion that the shooting was an accident.

“Don’t believe that Peter Liang didn’t know someone was there,” Mr. Alexis said, arguing that though it was dark, anyone in the stairwell would have been silhouetted by light from a hallway pouring in when Officer Liang opened the door. “The only thing that could have startled him was Akai Gurley and Melissa Butler.”

He added that Mr. Liang was looking for the bullet casing, which could be used to identify the gun from which it came, to “cover up” what he had done.

During a break on Tuesday, Mr. Gurley’s aunt, Hertencia Peterson, who has attended every day of the trial, stood with several women, discussing the case. They seemed focused not on what did happen the night of the shooting, but what did not. “He didn’t even check his pulse,” one of the women said of Officer Liang. “He did nothing to help!”

A version of this article appears in print on , Section A, Page 17 of the New York edition with the headline: Officer Aimed at Man in Stairwell, Prosecution Argues. Order Reprints | Today’s Paper | Subscribe